Generalized Cohomological Field Theories in the Higher Order Formalism

In the classical Batalin–Vilkovisky formalism, BV operator $$\Delta $$ is a differential of order two with respect to commutative product. graded setting, it known that if homotopically trivial, then there tree level cohomological field theory induced on homology; this manifestation fact homotopy quotient operad algebras by represented hypercommutative algebras. paper, we study generalized where given finite order. case, unravel new interesting algebraic structure homology whenever trivial. We also suggest sequence structures arising in higher formalism part “trinity” remarkable mathematical objects, fitting philosophy proposed Arnold 1990s.